The presence of a considerable amount of field curvature is a relatively basic feature of most refractive lens systems. However, there are certain applications where a flat field is necessary. Two examples of such applications are photographic objectives and to a somewhat lesser extent endoscope transfer optics. Unfortunately, field curvature is one of the hardest aberrations to correct, requiring increases in the complexity of the lens far in excess of those required to correct spherical and chromatic aberrations. While optical transfer systems typically do not require the same level of field curvature correction as photographic objectives, multiple transfer systems (field lenses as well as relay lenses) are much harder to correct. Thus, considerable effort has gone into designing lenses characterized by flat fields.
Petzval has shown that the field curvature is related to the so-called Petzval sum, P, which is given by: ##EQU1## where .phi..sub.i is the power of the ith refractive surface; and n.sub.i is the refractive index at the ith surface. More particularly, in absence of astigmatism, the field curvature is equal to -P. Thus, the radius of curvature of the field of a single lens of unit power is equal to -1/P=-n which represents a strongly curved field. In the case of multiple element lens systems, the Petzval sum strongly tends to be positive because the lens power is positive.
There are three basic methods of correcting the field curvature (reducing the Petzval sum), namely spacing, bending, and index difference. Each has been heralded as a milestone in the design of flat field lenses, and retains its importance today. The first method (spacing) is exemplified by the famous Cooke triplet form designed by H. Dennis Taylor and disclosed in U.S. Pat. No. 568,052. This method is based on the simple idea that an objective comprising a positive lens and a negative lens of equal and opposite powers and the same refractive index has a Petzval sum equal to 0, with the overall power of the system being determined by the separation of the elements. The actual triplet configuration is necessitated by the need to correct other aberrations.
The second basic method of correcting the field curvature (bending) is exemplified in the Hypergon designed by Goerz and disclosed in U.S. Pat. No. 706,650. This method utilizes bending of the elements. In this context, a purely unbent element has equal and opposite curvatures on both sides while the archetypical bent element has equal curvatures on both surfaces. It is noted that such a bent element having equal curvatures at its opposite surfaces represents spaced positive and negative surfaces of equal power and index, so that the Petzval sum vanishes with the overall power being provided by the separation of the two surfaces. Thus, bending represents a special case of separation within a single element. The use of bending to correct the field curvature is the basis of the double Gauss lens which continues to be a lens type of prime importance.
The third basic method of correcting the field curvature (index difference) is the so-called "new achromat" principle, utilizing differences of the refractive indices of the positive and negative elements. This principle, while recognized in the past, has presented problems that have hindered its usefulness. For example, the use of index difference in order to correct the Petzval sum requires the elements to have indices that differ in the opposite direction from what is required to correct spherical aberration. Thus, bent and spaced elements have had to be incorporated into any design attempting to use index difference.
It is possible to conceptualize the situation from a slightly different viewpoint. Rather than viewing the use of spacing, bending, and index difference as means for correcting the field curvature, one may equivalently recognize that the field curvature is largely independent of spacing, bending and index difference. Accordingly, one can select elements such that the Petzval sum vanishes, and then use bending, spacing and index difference to generate the overall power.
Most lens designs utilize a combination of the three methods. Although not previously recognized, a highly meaningful system of lens classification can be based on the relative importance of bending, spacing, and index difference as used to correct the Petzval sum (or generate power). Thus, as will be described below, it is possible to break up the Petzval sum correction into contributions by the various methods, and glean from the relative magnitudes of the individual contributions meaningful information relating to the inner workings of the lens.
It will be recognized that the use of spacing and bending to achieve a flat field lens presents certain problems. For example, when many elements have to be spaced, the system becomes very sensitive to tilt and decentration of the elements, and requires great precision in the lens mounting. In fact, spacing is effective only for relatively high powered components, which increases the criticality of the spacing. Sharply bent elements suffer from the problem that they are expensive to fabricate since only a small number of elements may be placed on the spherical grinding or polishing blocks used during fabrication. Accordingly, flat field lenses have tended to be expensive, both in their elements and in their mounts.